In
set theory, the random algebra or random real algebra is the
Boolean algebra of
Borel sets of the unit interval modulo the
ideal
Ideal may refer to:
Philosophy
* Ideal (ethics), values that one actively pursues as goals
* Platonic ideal, a philosophical idea of trueness of form, associated with Plato
Mathematics
* Ideal (ring theory), special subsets of a ring considere ...
of measure zero sets. It is used in random forcing to add random reals to a
model of set theory. The random algebra was studied by
John von Neumann in 1935 (in work later published as ) who showed that it is not isomorphic to the
Cantor algebra of Borel sets modulo
meager sets. Random forcing was introduced by .
See also
*
Random number
In mathematics and statistics, a random number is either Pseudo-random or a number generated for, or part of, a set exhibiting statistical randomness.
Algorithms and implementations
A 1964-developed algorithm is popularly known as ''the Knuth s ...
References
*
*
*
*
Boolean algebra
Forcing (mathematics)
{{Settheory-stub